OpenRaiser/Intern-Atlas huggingface dataset:
Generalized partially bent functions
Venue: arXiv cs.CR 2005
Year: 2005

Based on the definition of generalized partially bent functions, using the theory of linear transformation, the relationship among generalized partially bent functions over ring Z N, generalized bent functions over ring Z N and affine functions is discussed. When N is a prime number, it is proved that a generalized partially bent function can be decomposed as the addition of a generalized bent function and an affine function. The result obtained here generalizes the main works concerning partially bent functions by Claud Carlet in [1].
Computation of the Ramsey Number $R(W_5,K_5)$
Venue: arXiv cs.DM 2005
Year: 2005

We determine the value of the Ramsey number $R(W_5,K_5)$ to be 27, where $W_5 = K_1 + C_4$ is the 4-spoked wheel of order 5. This solves one of the four remaining open cases in the tables given in 1989 by George R. T. Hendry, which included the Ramsey numbers $R(G,H)$ for all pairs of graphs $G$ and $H$ having five vertices, except seven entries. In addition, we show that there exists a unique up to isomorphism critical Ramsey graph for $W_5$ versus $K_5$. Our results are based on computer algorithms.
Spatial Precoder Design for Space-Time Coded MIMO Systems: Based on Fixed Parameters of MIMO Channels
Venue: arXiv cs.IT 2005
Year: 2005

In this paper, we introduce the novel use of linear spatial precoding based on fixed and known parameters of multiple-input multiple-output (MIMO) channels to improve the performance of space-time coded MIMO systems. We derive linear spatial precoding schemes for both coherent (channel is known at the receiver) and non-coherent (channel is un-known at the receiver) space-time coded MIMO systems. Antenna spacing and antenna placement (geometry) are considered as fixed parameters of MIMO channels, which are readily known at the transmitter. These precoding schemes exploit the antenna placement information at both ends of the MIMO channel to ameliorate the effect of non-ideal antenna placement on the performance of space-time coded systems. In these schemes, the precoder is fixed for given transmit and receive antenna configurations and transmitter does not require any feedback of channel state information (partial or full) from the receiver. Closed form solutions for both precoding schemes are presented for systems with up to three receiver antennas. A generalized method is proposed for more than three receiver antennas. We use the coherent space-time block codes (STBC) and differential space-time block codes to analyze the performance of proposed precoding schemes. Simulation results show that at low SNRs, both precoders give significant performance improvement over a non-precoded system for small antenna aperture sizes.
Irreducible Frequent Patterns in Transactional Databases
Venue: arXiv cs.DS 2005
Year: 2005

Irreducible frequent patters (IFPs) are introduced for transactional databases. An IFP is such a frequent pattern (FP),(x1,x2,...xn), the probability of which, P(x1,x2,...xn), cannot be represented as a product of the probabilities of two (or more) other FPs of the smaller lengths. We have developed an algorithm for searching IFPs in transactional databases. We argue that IFPs represent useful tools for characterizing the transactional databases and may have important applications to bio-systems including the immune systems and for improving vaccination strategies. The effectiveness of the IFPs approach has been illustrated in application to a classification problem.
Distributed Navigation Algorithms for Sensor Networks
Venue: arXiv cs.NI 2005
Year: 2005

We propose efficient distributed algorithms to aid navigation of a user through a geographic area covered by sensors. The sensors sense the level of danger at their locations and we use this information to find a safe path for the user through the sensor field. Traditional distributed navigation algorithms rely upon flooding the whole network with packets to find an optimal safe path. To reduce the communication expense, we introduce the concept of a skeleton graph which is a sparse subset of the true sensor network communication graph. Using skeleton graphs we show that it is possible to find approximate safe paths with much lower communication cost. We give tight theoretical guarantees on the quality of our approximation and by simulation, show the effectiveness of our algorithms in realistic sensor network situations.
Computing shortest non-trivial cycles on orientable surfaces of bounded genus in almost linear time
Venue: arXiv cs.CG 2005
Year: 2005

We present an algorithm that computes a shortest non-contractible and a shortest non-separating cycle on an orientable combinatorial surface of bounded genus in O(n \log n) time, where n denotes the complexity of the surface. This solves a central open problem in computational topology, improving upon the current-best O(n^{3/2})-time algorithm by Cabello and Mohar (ESA 2005). Our algorithm uses universal-cover constructions to find short cycles and makes extensive use of existing tools from the field.
Analytical Bounds on Maximum-Likelihood Decoded Linear Codes with Applications to Turbo-Like Codes: An Overview
Venue: arXiv cs.IT 2005
Year: 2005

Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and their relation to a variety of other reported bounds. Within the class of lower bounds, we address de Caen's based bounds and their improvements, sphere-packing bounds, and information-theoretic bounds on the bit error probability of codes defined on graphs. A comprehensive overview is provided in a monograph by the authors which is currently in preparation.
De Dictionariis Dynamicis Pauco Spatio Utentibus
Venue: arXiv cs.DS 2005
Year: 2005

We develop dynamic dictionaries on the word RAM that use asymptotically optimal space, up to constant factors, subject to insertions and deletions, and subject to supporting perfect-hashing queries and/or membership queries, each operation in constant time with high probability. When supporting only membership queries, we attain the optimal space bound of Theta(n lg(u/n)) bits, where n and u are the sizes of the dictionary and the universe, respectively. Previous dictionaries either did not achieve this space bound or had time bounds that were only expected and amortized. When supporting perfect-hashing queries, the optimal space bound depends on the range {1,2,...,n+t} of hashcodes allowed as output. We prove that the optimal space bound is Theta(n lglg(u/n) + n lg(n/(t+1))) bits when supporting only perfect-hashing queries, and it is Theta(n lg(u/n) + n lg(n/(t+1))) bits when also supporting membership queries. All upper bounds are new, as is the Omega(n lg(n/(t+1))) lower bound.
Mathematical Models in Schema Theory
Venue: arXiv cs.AI 2005
Year: 2005

In this paper, a mathematical schema theory is developed. This theory has three roots: brain theory schemas, grid automata, and block-shemas. In Section 2 of this paper, elements of the theory of grid automata necessary for the mathematical schema theory are presented. In Section 3, elements of brain theory necessary for the mathematical schema theory are presented. In Section 4, other types of schemas are considered. In Section 5, the mathematical schema theory is developed. The achieved level of schema representation allows one to model by mathematical tools virtually any type of schemas considered before, including schemas in neurophisiology, psychology, computer science, Internet technology, databases, logic, and mathematics.
The Complexity of Poor Man's Logic
Venue: arXiv cs.LO 2005
Year: 2005

Motivated by description logics, we investigate what happens to the complexity of modal satisfiability problems if we only allow formulas built from literals, $\wedge$, $\Diamond$, and $\Box$. Previously, the only known result was that the complexity of the satisfiability problem for K dropped from PSPACE-complete to coNP-complete (Schmidt-Schauss and Smolka, 1991 and Donini et al., 1992). In this paper we show that not all modal logics behave like K. In particular, we show that the complexity of the satisfiability problem with respect to frames in which each world has at least one successor drops from PSPACE-complete to P, but that in contrast the satisfiability problem with respect to the class of frames in which each world has at most two successors remains PSPACE-complete. As a corollary of the latter result, we also solve the open problem from Donini et al.'s complexity classification of description logics (Donini et al., 1997). In the last section, we classify the complexity of the satisfiability problem for K for all other restrictions on the set of operators.
Linear-Time Pointer-Machine Algorithms for Path-Evaluation Problems on Trees and Graphs
Venue: arXiv cs.DS 2006
Year: 2006

We present algorithms that run in linear time on pointer machines for a collection of problems, each of which either directly or indirectly requires the evaluation of a function defined on paths in a tree. These problems previously had linear-time algorithms but only for random-access machines (RAMs); the best pointer-machine algorithms were super-linear by an inverse-Ackermann-function factor. Our algorithms are also simpler, in some cases substantially, than the previous linear-time RAM algorithms. Our improvements come primarily from three new ideas: a refined analysis of path compression that gives a linear bound if the compressions favor certain nodes, a pointer-based radix sort as a replacement for table-based methods, and a more careful partitioning of a tree into easily managed parts. Our algorithms compute nearest common ancestors off-line, verify and construct minimum spanning trees, do interval analysis on a flowgraph, find the dominators of a flowgraph, and build the component tree of a weighted tree.
Survey propagation: an algorithm for satisfiability
Venue: arXiv cs.CC 2006
Year: 2006

We study the satisfiability of randomly generated formulas formed by $M$ clauses of exactly $K$ literals over $N$ Boolean variables. For a given value of $N$ the problem is known to be most difficult with $α=M/N$ close to the experimental threshold $α_c$ separating the region where almost all formulas are SAT from the region where all formulas are UNSAT. Recent results from a statistical physics analysis suggest that the difficulty is related to the existence of a clustering phenomenon of the solutions when $α$ is close to (but smaller than) $α_c$. We introduce a new type of message passing algorithm which allows to find efficiently a satisfiable assignment of the variables in the difficult region. This algorithm is iterative and composed of two main parts. The first is a message-passing procedure which generalizes the usual methods like Sum-Product or Belief Propagation: it passes messages that are surveys over clusters of the ordinary messages. The second part uses the detailed probabilistic information obtained from the surveys in order to fix variables and simplify the problem. Eventually, the simplified problem that remains is solved by a conventional heuristic.
Goedel Machines: Self-Referential Universal Problem Solvers Making Provably Optimal Self-Improvements
Venue: arXiv cs.LO 2006
Year: 2006

We present the first class of mathematically rigorous, general, fully self-referential, self-improving, optimally efficient problem solvers. Inspired by Kurt Goedel's celebrated self-referential formulas (1931), such a problem solver rewrites any part of its own code as soon as it has found a proof that the rewrite is useful, where the problem-dependent utility function and the hardware and the entire initial code are described by axioms encoded in an initial proof searcher which is also part of the initial code. The searcher systematically and efficiently tests computable proof techniques (programs whose outputs are proofs) until it finds a provably useful, computable self-rewrite. We show that such a self-rewrite is globally optimal - no local maxima! - since the code first had to prove that it is not useful to continue the proof search for alternative self-rewrites. Unlike previous non-self-referential methods based on hardwired proof searchers, ours not only boasts an optimal order of complexity but can optimally reduce any slowdowns hidden by the O()-notation, provided the utility of such speed-ups is provable at all.
Phantom Types and Subtyping
Venue: arXiv cs.PL 2006
Year: 2006

We investigate a technique from the literature, called the phantom-types technique, that uses parametric polymorphism, type constraints, and unification of polymorphic types to model a subtyping hierarchy. Hindley-Milner type systems, such as the one found in Standard ML, can be used to enforce the subtyping relation, at least for first-order values. We show that this technique can be used to encode any finite subtyping hierarchy (including hierarchies arising from multiple interface inheritance). We formally demonstrate the suitability of the phantom-types technique for capturing first-order subtyping by exhibiting a type-preserving translation from a simple calculus with bounded polymorphism to a calculus embodying the type system of SML.
Contextual equivalence for higher-order pi-calculus revisited
Venue: arXiv cs.PL 2006
Year: 2006

The higher-order pi-calculus is an extension of the pi-calculus to allow communication of abstractions of processes rather than names alone. It has been studied intensively by Sangiorgi in his thesis where a characterisation of a contextual equivalence for higher-order pi-calculus is provided using labelled transition systems and normal bisimulations. Unfortunately the proof technique used there requires a restriction of the language to only allow finite types. We revisit this calculus and offer an alternative presentation of the labelled transition system and a novel proof technique which allows us to provide a fully abstract characterisation of contextual equivalence using labelled transitions and bisimulations for higher-order pi-calculus with recursive types also.
Bayesian Restoration of Digital Images Employing Markov Chain Monte Carlo a Review
Venue: arXiv cs.CV 2006
Year: 2006

A review of Bayesian restoration of digital images based on Monte Carlo techniques is presented. The topics covered include Likelihood, Prior and Posterior distributions, Poisson, Binay symmetric channel, and Gaussian channel models of Likelihood distribution,Ising and Potts spin models of Prior distribution, restoration of an image through Posterior maximization, statistical estimation of a true image from Posterior ensembles, Markov Chain Monte Carlo methods and cluster algorithms.
Computing finite-dimensional bipartite quantum separability
Venue: arXiv cs.DS 2006
Year: 2006

Ever since entanglement was identified as a computational and cryptographic resource, effort has been made to find an efficient way to tell whether a given density matrix represents an unentangled, or separable, state. Essentially, this is the quantum separability problem. Chapters 1 to 3 motivate a new interior-point algorithm which, given the expected values of a subset of an orthogonal basis of observables of an otherwise unknown quantum state, searches for an entanglement witness in the span of the subset of observables. When all the expected values are known, the algorithm solves the separability problem. In Chapter 4, I give the motivation for the algorithm and show how it can be used in a particular physical scenario to detect entanglement (or decide separability) of an unknown quantum state using as few quantum resources as possible. I then explain the intuitive idea behind the algorithm and relate it to the standard algorithms of its kind. I end the chapter with a comparison of the complexities of the algorithms surveyed in Chapter 3. Finally, in Chapter 5, I present the details of the algorithm and discuss its performance relative to standard methods.
Dynamic Asymmetric Communication
Venue: arXiv cs.IT 2006
Year: 2006

We show how any dynamic instantaneous compression algorithm can be converted to an asymmetric communication protocol, with which a server with high bandwidth can help clients with low bandwidth send it messages. Unlike previous authors, we do not assume the server knows the messages' distribution, and our protocols are the first to use only one round of communication for each message.
Neyman-Pearson Detection of Gauss-Markov Signals in Noise: Closed-Form Error Exponent and Properties
Venue: arXiv cs.IT 2006
Year: 2006

The performance of Neyman-Pearson detection of correlated stochastic signals using noisy observations is investigated via the error exponent for the miss probability with a fixed level. Using the state-space structure of the signal and observation model, a closed-form expression for the error exponent is derived, and the connection between the asymptotic behavior of the optimal detector and that of the Kalman filter is established. The properties of the error exponent are investigated for the scalar case. It is shown that the error exponent has distinct characteristics with respect to correlation strength: for signal-to-noise ratio (SNR) >1 the error exponent decreases monotonically as the correlation becomes stronger, whereas for SNR <1 there is an optimal correlation that maximizes the error exponent for a given SNR.
f2mma: FORTRAN to Mathematica translator
Venue: arXiv cs.OH 2006
Year: 2006

f2mma program can be used to translate programs written in some subset of the FORTRAN language into {\sl Mathematica} system's programming language. This subset have been enough to translate GAPP (Global Analysis of Particle Properties) programm into {\sl Mathematica} language automatically. Observables table calculated with GAPP({\sl Mathematica}) is presented.
Model Checking Probabilistic Pushdown Automata
Venue: arXiv cs.LO 2006
Year: 2006

We consider the model checking problem for probabilistic pushdown automata (pPDA) and properties expressible in various probabilistic logics. We start with properties that can be formulated as instances of a generalized random walk problem. We prove that both qualitative and quantitative model checking for this class of properties and pPDA is decidable. Then we show that model checking for the qualitative fragment of the logic PCTL and pPDA is also decidable. Moreover, we develop an error-tolerant model checking algorithm for PCTL and the subclass of stateless pPDA. Finally, we consider the class of omega-regular properties and show that both qualitative and quantitative model checking for pPDA is decidable.
OpenVanilla - A Non-Intrusive Plug-In Framework of Text Services
Venue: arXiv cs.HC 2006
Year: 2006

Input method (IM) is a sine qua non for text entry of many Asian languages, but its potential applications on other languages remain under-explored. This paper proposes a philosophy of input method design by seeing it as a nonintrusive plug-in text service framework. Such design allows new functionalities of text processing to be attached onto a running application without any tweaking of code. We also introduce OpenVanilla, a cross-platform framework that is designed with the above-mentioned model in mind. Frameworks like OpenVanilla have shown that an input method can be more than just a text entry tool: it offers a convenient way for developing various text service and language tools.
A formally verified proof of the prime number theorem
Venue: arXiv cs.AI 2006
Year: 2006

The prime number theorem, established by Hadamard and de la Vall'ee Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1 / ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erd"os in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.
Grid Vertex-Unfolding Orthogonal Polyhedra
Venue: arXiv cs.CG 2006
Year: 2006

An edge-unfolding of a polyhedron is produced by cutting along edges and flattening the faces to a *net*, a connected planar piece with no overlaps. A *grid unfolding* allows additional cuts along grid edges induced by coordinate planes passing through every vertex. A vertex-unfolding permits faces in the net to be connected at single vertices, not necessarily along edges. We show that any orthogonal polyhedron of genus zero has a grid vertex-unfolding. (There are orthogonal polyhedra that cannot be vertex-unfolded, so some type of "gridding" of the faces is necessary.) For any orthogonal polyhedron P with n vertices, we describe an algorithm that vertex-unfolds P in O(n^2) time. Enroute to explaining this algorithm, we present a simpler vertex-unfolding algorithm that requires a 3 x 1 refinement of the vertex grid.
Capacity with Causal and Non-Causal Side Information - A Unified View
Venue: arXiv cs.IT 2006
Year: 2006

We identify the common underlying form of the capacity expression that is applicable to both cases where causal or non-causal side information is made available to the transmitter. Using this common form we find that for the single user channel, the multiple access channel, the degraded broadcast channel, and the degraded relay channel, the sum capacity with causal and non-causal side information are identical when all the transmitter side information is also made available to all the receivers. A genie-aided outerbound is developed that states that when a genie provides $n$ bits of side information to a receiver the resulting capacity improvement can not be more than $n$ bits. Combining these two results we are able to bound the relative capacity advantage of non-causal side information over causal side information for both single user as well as various multiple user communication scenarios. Applications of these capacity bounds are demonstrated through examples of random access channels. Interestingly, the capacity results indicate that the excessive MAC layer overheads common in present wireless systems may be avoided through coding across multiple access blocks. It is also shown that even one bit of side information at the transmitter can result in unbounded capacity improvement. As a side, we obtain the sum capacity for a multiple access channel when the side information available to the transmitter is causal and possibly correlated to the side information available to the receiver.